Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock
(Updated Aug. 8, 2012)
These notes provide a technical brief on the definitions of numeric readouts in Mars24. Further details can be found in the appended references. A less technical account of solar time on Mars is provided in the 1998 article "Telling Time on Mars" on the NASA GISS website. Information about the specific controls and displays in Mars24 is provided in the accompanying User's Guide.
Mars Solar Days and 24-hr Clock Convention
Following the long-standing practice originally adopted in 1976 by the Viking Lander missions, the daily variation of Mars solar time is reckoned in terms of a "24-hour" clock, representing a 24-part division of the planet's solar day, along with the traditional sexagesimal subdivisions of 60 minutes and 60 seconds. A Mars solar day has a mean period of 24 hours 39 minutes 35.244 seconds, and is customarily referred to as a "sol" in order to distinguish this from the roughly 3% shorter solar day on Earth. The Mars sidereal day, as measured with respect to the fixed stars, is 24h 37m 22.663s, as compared with 23h 56m 04.0905s for Earth.
Mars Solar Seasons
The apparent seasonal advance of the Sun at Mars is commonly measured in terms of the areocentric longitude Ls, as referred to the planet's vernal equinox (the ascending node of the apparent seasonal motion of the Sun on the planet's equator). As defined, Ls = 0°, 90°, 180°, and 270° indicate the Mars northern hemisphere vernal equinox, summer solstice, autumnal equinox, and winter solstice, respectively.
In terms of Ls, the seasonally variable, planet-centered solar declination d equals arcsin [(sin e)(sin Ls)], where the obliquity e is the inclination of the planet's spin axis with respect to the plane of its orbit. For an accurate account of the solar illumination relative to the plane of a locally flat surface, the solar declination can be corrected for the small difference appropriate to the so-called planetographic measure of latitude on an oblate sphere, as it is in the Mars24 sunclock.
As a result of the Mars's orbital eccentricity, Ls advances somewhat unevenly with time, but can be efficiently evaluated as a trigonometric power series for the orbital eccentricity and the orbital mean anomaly measured with respect to the perihelion. The areocentric longitude at perihelion, Ls,p = 251°.000 + 0°.00645×(yr - 2000), indicates a near alignment of the planet's closest approach to the Sun in its orbit with its winter solstice season, as related to the occasional onset of global dust storms within the advance of this season.
Mars Orbit Periods
The period for the repetition of the planet-centered measure of mean Solar longitude is referred to as the tropical year. (This period is linked to the rate of advance of the "Fictitious Mean Sun," as discussed below.) The Mars tropical year is 686.9726 day or 668.5921 sol. For comparison, the Mars sidereal year, as measured with respect to the fixed stars, is 668.5991 sol. The difference between these values results from the precession of the planet's spin axis.
The mean interval between the repetition of the planet's perihelion passage, or anomalistic year, is 668.6146 sol, and corresponds to the rate of advance of the planet's orbital mean anomaly. The mean repetition period for a particular solar season varies with the Ls. The mean repetition intervals for the vernal equinox, summer solstice, autumnal equinox, and winter solstice on Mars are 668.5906 sol, 668.5880 sol, 668.5940 sol, and 668.5958 sol, respectively, and the average of these is just the tropical year.
Mean and True Solar Time
Also as a result of a planet's orbital eccentricity, as well as its obliquity, there is a seasonally variable discrepancy between the even advance of an artificially defined Mean Solar Time and of the True Solar Time corresponding to the actual planet-centered position of the Sun in its sky. Following the conventional usage of terrestrial timekeeping, Mean Solar Time on Mars has been defined in reference to the so-called Right Ascension of the Fictitious Mean Sun (FMS). As defined, the FMS is the angle between the planet's vernal equinox, measured along the plane of its equator, and an artificially defined "dynamical mean Sun" advancing at a rate corresponding to the planet's solar tropical year (i.e., the Mars FMS advances at a rate of 360°/686.9726 day or 0.5240384°/day). Its numerical value (to within an arbitrary multiple of 360°) is just the sum of the orbital mean anomaly, M, and the areocentric longitude at perihelion, Ls,p. The FMS at Mars was evaluated by Allison and McEwen (2000) (hereafter "AM2000") as a mean fit to an accurate calculation of the areocentric longitude over 134 Mars orbits (for the years 1874-2127), adjusted in its angular placement by the (~0°.0046) solar aberration. This evaluation has been adopted by the Mars Exploration Rover project for its definition of Mars Mean Solar Time (cf. Roncoli et al., 2002).
The difference between the True Solar Time (TST) and the Mean Solar Time (MST), equivalent in the corresponding angular measure to the difference between the right ascensions of the FMS and the true Sun, is referred to as the Equation of Time (EOT). For Earth, the EOT varies between -14.2min and +16.3min. Mars, with its more than five times larger orbital eccentricity, has an EOT varying between -51.1min and +39.9min. The parametric plot of the EOT vs. the solar declination is called the solar analemma. For Earth, this takes the form of the figure-8 pattern marked on some sundials and globes (for the latter typically in the empty space of the South Pacific). For Mars, the analemma assumes the shape of a raindrop or mis-shapen pear.
Local and "Zonal" Times
In the mid-1800s the use of locally measured and defined time on Earth was gradually supplanted by the use of time zones in order to facilitate standardization of railroad schedules and, to a lesser extent, of recording scientific observations. This process culminated in 1884 in an international conference which created the global system of time zones and specified the longitude of Greenwich as the prime meridian. Each zone is approximately 15° wide, the exact width and shape being subject to political boundaries and significant geographic features, and within each clocks are referenced to the same hour.
The prime meridian of Mars is defined by the location of the crater Airy-0 (De Vaucoulers et al., 1973), named in honor of the British astronomer George Biddel Airy, who built the telescope at Greenwich whose location defines the prime meridian on Earth. The Mars24 application thus refers to "standard" time on the Mars prime meridian as "Airy Mean Time" (AMT) in analogy to Earth's "Greenwich Mean Time" (GMT), although the latter term has been supplanted by the more accurate Coordinated Universal Time (UTC) in international timekeeping services.
Mars24 includes the option to display the local time at the selected location in terms of similarly constructed "Mars time zones". We have defined these Mars time zones to be exactly 15° wide and centered on successive 15° multiples of longitude, at 0°, 15°, 30°, etc. We have not attempted to name these time zones, as for example "Olympus Standard Time", but do identify their read-out with a suffix indicating the timezone offset. Thus, for the the case of Olympus Mons the timezone identifier is "AMT-9", or nine hours behind Airy Mean Time.
Each landed mission on Mars has adopted a different reference for its solar time keeping and mission clock.
The Viking Lander "Sol Numbers" were reckoned from a zero starting point at each of the local true solar midnights immediately prior to their touchdowns.
Time tags for the Mars Pathfinder Lander were referenced with respect to the Local True Solar Time (LTST), with elapsed sols reckoned from the local true solar midnight preceding its landing, but designated with a starting number "1" rather than from "0". Conversion formulae are provided by AM2000.
The derivation of mission time adopted by the Mars Exploration Rover Project by mission controllers at the NASA Jet Propulsion Laboratory is an offset modification of an evenly advancing mean solar time, based on its definition by Roncoli et al. (2002). For MER-A Spirit, the difference between lander mission time and Local Mean Solar Time (LMST) is more than 41 minutes; for MER-B Opportunity the difference is more than 37 minutes. The intention was that at approximately the middle of each of the MER A and B nominal missions (i.e., on the 45th sol after landing), lander mission time should align with Local True Solar Time to within 30 seconds. As with Pathfinder, "Sol 1" for each MER lander denotes the solar day on which the individual lander touched down on the Martian surface.
The Mars Phoenix lander mission reverted to using Sol 0 to indicate the solar day on which the lander touched down. Mission controllers originally specified a mission clock based on the Local Mean Solar Time at the landing site, designated "DAB1" and located at 233.35°E. Thus, official mission time specified the Sol 0 epoch would start at local mean midnight at 233.35°E prior to landing. However, there was a late decision to shift the landing to site "CSZ_032708", located at 234.24845°E, but to continue using a mission clock aligned with the DAB1 site. This would have resulted in a de facto mission clock offset from LMST by about two and half minutes. In actuality, Phoenix landed 5 km off target from CSZ_032708, at 234.24845°E. Thus, the end result was that mission time and LMST differ by three and a half minutes.
The Mars Science Laboratory rover project also defined Sol 0 as the solar day on which the lander would touch down. Mission controllers originally specified a mission clock based on the Local Mean Solar Time for a landing site at 137.42°E. Thus, official mission time specified the Sol 0 epoch would start at local mean midnight at 137.42°E prior to landing. However, as the landing site coordinates were later refined, after course corrections were made while MSL Curiosity was in-flight to Mars, and as the rover touched down somewhat "long" of the final target coordinates, the landing site turned out to be at 137.441635°E. Following the example of Phoenix, there was no re-definition of the MSL mission clock to match the actual landing coordinates, and so a difference of a several seconds between LMST at the landing site and mission clock resulted.
Mars Sol Date (MSD)
Although numerous month-year calendars have been proposed for Mars, we have not attempted to support any of these as a feature of Mars24. We have, however, included in the Mars24 displays the "Mars Sol Date" (MSD) defined by AM2000. This represents a sequential count of Mars solar days elapsed since 1873 December 29 at approximately Greenwich noon (Julian Date 2405522.0). This epoch was prior to the great 1877 perihelic opposition of Mars and precedes nearly all detailed observations of temporal changes on the planet. It corresponds to a Mars Ls of 277°, approximately the same planetocentric solar longitude as that for the Earth on the same date. MSD 44796.0 is approximately coincident with 2000 January 6.0, at a near-coincidence of prime meridian midnights on the two planets and a repetition of Mars Ls = 277°. The period 44796 sols also represents a near commensurability of 126 Julian years and 67 Mars tropical revolutions. In principle, the MSD could be used as a coherent sol-date reference for a variety of Mars missions.
Mars24 uses the short-series representation of the seven-largest short-period planetary perturbations of the Mars orbital longitude specified by AM2000, as adapted from Simon et al. (1994). Detailed comparisons with an accurate ephemeris suggest that the maximum error in the calculated Ls by the adopted algorithm is 0°.008 over ±100 years of J2000. According to the implicit dependence of the calculated EOT on the Ls, the resulting True Solar Time (TST) can be estimated to be in error by as much as 3sec. The error in the currently coded conversion between TT and UTC is itself in error for some periods in the post-1975 era by as much as 3sec. There is also as yet a small (~0°.004) uncertainty in the inertial location of the Mars prime meridian as defined by the crater Airy-0 (Duxbury et al., 2001).
Of course, the calculation of Local (True or Mean) solar time cannot be any more accurate than the longitudinal placement of the local point of interest! Predicted solar times for a given lander location may therefore need to be revised as improved knowledge of their locations becomes available. Although the precise coordinates of the two MER landers were obtained quickly after their landing, disputes as to the precise locations of the two Viking landers continued for more than 20 years.
Mars24's estimate of times of local sunrise and sunset, as well as times of Earthrise and Earthset, requires correct input of latitude. Even so, the results may be in error due to local topography and atmospheric refraction. Comparison to known times for a limited number of solar and Earth rise and set events at Mars lander sites suggest that absent topographic and atmospheric effects, the error in calculating these times is less than 30 seconds.